25 Nov
2004
25 Nov
'04
10:35 a.m.
Dear Cat Community, I have the following question about preservation of properties of fiber categories in the total category: Given a contravariant indexed category F : B^Op -> Cat, and the Grothendieck translation from the indexed category to fibrations Flat(F). Then, the first projection P : Flat(F) -> B forms a (split) fibration, called the flattening of F. Now assume that the fiber categories are complete/cocomplete/adhesive. Would it be the case that the total category Flat(F) of the described (split) fibration is also complete/cocomplete/adhesive? Any references would be appreciated. Thank you kindly. Best regards, Alexey Cherchago 25-Nov-2004 14:18:16 -0400,2139;000000000000-00000000